Finite Group DatabasebetaFinite Group Databasebeta| order | 19584 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8257536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C9×C16×C17 |
| multiplicative | (ℤ/41752)ˣ, (ℤ/43928)ˣ, (ℤ/58944)ˣ, (ℤ/62424)ˣ, (ℤ/62628)ˣ, (ℤ/65892)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C24×C3×C17 |
| socle, prime radical | C24×C3×C17 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1320 conjugacy classes of subgroups.
19584 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.